The answer depends on the type of azalea. Some are more cold-hardy than others. In general, azaleas will be fine in the 40s. Even a hard frost, although it may damage or discolor some leaves, won't kill the plant.

However, there are some species that can be affected, especially in the spring. What can happen is that an azalea that has successfully wintered in sub-freezing temperatures will begin to sense the onset of spring and run its sap before nature has finished sending sub-freezing temperatures at it. This means the bark has fluid transferring within it as the plant gears up for spring that was not present during the winter. Then, if a late freeze occurs, the sap freezes which kills the bark, literally tearing it up at the cellular level.

The results of this damage are not immediately apparent. It may take months or even seasons to notice, but you will see the bark, mainly near the soil surface, start to split and/or peel away from the trunk. That means it has been damaged. If the area of damaged bark completely girdles the trunk, everything north of the girdle will die.